This work concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric study is fulfilled to study the effects of both the aspect ratio and the inhomogeneity parameters on the natural frequencies. The outcomes are presented in both graphical and tabular forms. It was seen that the fundamental frequency is principally affected from the inhomogeneity parameters than the higher ones. However, the natural frequencies except the fundamental ones are dramatically affected from the thickness of the sphere. It is also revealed that, there is a linear relationship between the fundamental frequency and others in higher modes of the same sphere under all boundary conditions.